Generalizing Born-Oppenheimer approximations and observable effects of an induced gauge field

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Abstract
By extending the Born-Oppenheimer approximation improved by Wilczek et al. to deal with separation of the spin and space coordinates of a particle in an external field, we generally discuss the direct effects of an induced gauge field and the higher-order corrections to the problem. It is shown that Bitter and Dubbers's experiment about Berry's phase is directly explained as an effect of the induced gauge potential in terms of the first-order approximation in this paper. The higher-order effects appearing in this experiment are also pointed out when the adiabatic conditions are broken.